%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC012+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:05:05 PM UTC 2026
% Result : Theorem 6.85s 3.50s
% Output : Proof 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 14 unt; 0 def)
% Number of atoms : 128 ( 46 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 156 ( 63 ~; 52 |; 30 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 19 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f83,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f83_nnf,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f83]) ).
fof(f83_sk,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f83_nnf]) ).
cnf(c176,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f83_sk]) ).
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> app(W,cons(X2,nil)) != X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f95_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> app(W,cons(X2,nil)) != X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [X2] :
( app(W,cons(X2,nil)) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Y,Z,X1] :
( ( ( ~ neq(sk50,nil)
& neq(sk48,nil) )
| ( app(sk49,cons(sk51,nil)) = sk50
& ssItem(sk51)
& ( app(Z,X1) != sk47
| app(app(Z,cons(Y,nil)),X1) != sk48
| ~ ssList(X1)
| ~ ssList(Z)
| ~ ssItem(Y) )
& neq(sk48,nil) ) )
& sk47 = sk49
& sk48 = sk50
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50,sk51])],[f95_nnf]) ).
cnf(c191,plain,
ssList(sk48),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p389,plain,
app(sk48,nil) = sk48,
inference(resolution,[status(thm)],[c176,c191]) ).
cnf(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p385,plain,
app(sk47,nil) = sk47,
inference(resolution,[status(thm)],[c176,c190]) ).
fof(f16,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f16_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c83,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c203,plain,
( ~ neq(sk50,nil)
| app(sk49,cons(sk51,nil)) = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p206,plain,
( ~ neq(sk48,nil)
| app(sk49,cons(sk51,nil)) = sk50 ),
inference(superposition,[status(thm)],[c194,c203]) ).
cnf(c196,plain,
( neq(sk48,nil)
| neq(sk48,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p205,plain,
neq(sk48,nil),
inference(factoring,[status(thm)],[c196]) ).
cnf(p207,plain,
app(sk49,cons(sk51,nil)) = sk50,
inference(resolution,[status(thm)],[p206,p205]) ).
cnf(p208,plain,
sk50 = sk48,
inference(superposition,[status(thm)],[c194,p207]) ).
cnf(c199,plain,
( ~ neq(sk50,nil)
| app(X5,X6) != sk47
| app(app(X5,cons(X4,nil)),X6) != sk48
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p209,plain,
( ~ neq(sk48,nil)
| app(X1,X2) != sk47
| app(app(X1,cons(X0,nil)),X2) != sk48
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[p208,c199]) ).
cnf(c201,plain,
( ~ neq(sk50,nil)
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p204,plain,
( ~ neq(sk48,nil)
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c194,c201]) ).
cnf(p212,plain,
ssItem(sk51),
inference(resolution,[status(thm)],[p204,p205]) ).
cnf(p214,plain,
( ~ neq(sk48,nil)
| app(X0,X1) != sk47
| app(app(X0,cons(sk51,nil)),X1) != sk48
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p209,p212]) ).
cnf(p228,plain,
( ~ neq(sk48,nil)
| app(sk47,X0) != sk47
| app(sk48,X0) != sk48
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p214,c190]) ).
cnf(p276,plain,
( ~ neq(sk48,nil)
| app(sk47,nil) != sk47
| app(sk48,nil) != sk48 ),
inference(resolution,[status(thm)],[c83,p228]) ).
cnf(p386,plain,
( ~ neq(sk48,nil)
| sk47 != sk47
| app(sk48,nil) != sk48 ),
inference(demodulation,[status(thm)],[p385,p276]) ).
cnf(p393,plain,
( ~ neq(sk48,nil)
| sk47 != sk47
| sk48 != sk48 ),
inference(demodulation,[status(thm)],[p389,p386]) ).
cnf(p394,plain,
( ~ neq(sk48,nil)
| sk47 != sk47 ),
inference(equality_resolution,[status(thm)],[p393]) ).
cnf(p396,plain,
~ neq(sk48,nil),
inference(equality_resolution,[status(thm)],[p394]) ).
cnf(p397,plain,
$false,
inference(resolution,[status(thm)],[p396,p205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC012+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 15:54:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.85/3.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.85/3.50 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------